Sen. John McCain, R-Ariz., center, speaks following a vote in the Senate on immigration reform on Capitol Hill in Washington on Thursday.

WASHINGTON — A historic immigration bill offering citizenship to 11 million undocumented immigrants passed the Senate on Thursday with bipartisan support and was sent to the House, where its prospects remained dim.

Senate Majority Leader Harry Reid ordered senators to their desks in the ornate chamber to vote on the “landmark legislation that will help secure our borders.”

“This historic legislation recognizes that today’s immigrants came for the right reasons — the same reasons as generations before them,” Reid said.

To underscore the significance of the Senate vote, Vice President Joe Biden presided over the chamber during the roll call vote.

The bill was passed on a 68-32 vote, falling just short of the 70 votes supporters had wanted to build momentum and force House Republican leaders to take up their bill.

But just hours earlier, House Speaker John Boehner, R-Ohio, said he would not bring the Senate bill to the House floor and instead would offer separate legislation currently being written by a House committee.

“We’re going to do our own bill, through regular order, and it’ll be legislation that reflects the will of our majority and the will of the American people,” Boehner said.

“Now the battle begins in the House,” said Rep. Joaquin Castro, D-San Antonio.

Senate Democrats voted en bloc for the sweeping immigration that increases visas for high-skilled and agricultural workers and doubles the size of the Border Patrol.

They were joined by 14 Republicans.

The bipartisan bill, written by four Democrats and four Republicans known as the Gang of Eight, was endorsed by the U.S. Chamber of Commerce and the AFL-CIO.

President Barack Obama said the bill did not include everything he wanted, but he backed the legislation and urged the House and Senate to quickly pass reform that he would sign into the law.

The Senate bill is the first rewrite of the nation’s complex immigration laws since 1986, when President Ronald Reagan signed legislation that granted citizenship to 3 million undocumented immigrants.

Republican leaders in the Senate said the increase in undocumented immigrants here now showed that the 1986 bill did not work.

House Republican leaders, like those in the Senate, are solidly against citizenship proposals for undocumented immigrants, which they label as amnesty for lawbreakers who entered the country illegally.

All Senate Republican leaders opposed the bill and urged their GOP colleagues in the House to use that as leverage as they write a more enforcement-centered bill.

Senate Republican Leader Mitch McConnell, R-Ky., said the Senate bill would never become law in its current form.

And Sen. John Cornyn, R-Texas, the Senate GOP whip, who voted against the bill, said he hoped the House would “rescue this bill by strengthening its security provisions.”

He said it contained a “loophole” that would give employers an incentive to hire undocumented workers to avoid paying health care premiums under the Affordable Care Act.

But backers of the Senate bill successfully turned back challenges to the legislation over three weeks of debate.

Sen. Patrick Leahy, D-Vt., the chairman of the Senate Judiciary Committee, said many of those challenges were raised by senators who “no matter what happened were going to vote against the legislation.”

One of the challenges was a sweeping amendment by Cornyn that required the Southwest border to be 100 percent secure before legal permanent status or citizenship could be granted to undocumented immigrants.

His measure was rejected.

Instead, the Senate passed a compromise amendment written by Sen. Bob Corker, R-Tenn., and Sen. John Hoeven, R-N.D., that would double the size of U.S. Customs and Border Protection.

And it kept intact the centerpiece, a measure that would allow the estimated 11 million undocumented immigrants in this country to receive legal permanent status and sets a 13-year pathway to citizenship.

Those eligible would be undocumented immigrants who pay fines and back taxes, learn English and clear criminal background checks.

House GOP leaders, meanwhile, have vowed to slow down the process — despite the party’s pledges to reach out to Latinos after the 2012 election, in which President Obama received 71 percent of the Hispanic vote.

But many Republicans in the House oppose citizenship proposals.

“Most Americans feel that legalizing millions of illegal immigrants would be a drain on government services,” said Rep. Lamar Smith, R-San Antonio.

Instead, the House Judiciary Committee is passing separate bills focusing on border security, enforcement and an increase in high-skilled workers sought by technology and specialized industries.

Smith’s legislation to expand the electronic verification system for employers to check immigration status of potential employees is one of the bills approved by the committee.

Rep. Sheila Jackson Lee, D-Houston, a ranking Democrat on the Judiciary Committee, said the piecemeal approach was not “comprehensive reform” and merely a GOP gimmick to slow down the process started in the Senate.